The polarizing impact of numeracy, economic literacy, and science literacy on the perception of immigration

Immigrants might be perceived as a threat to a country’s jobs, security, and cultural identity. In this study, we aimed to test whether individuals with higher numerical, scientific, and economic literacy were more polarized in their perception of immigration, depending on their cultural worldview orientation. We measured these variables in a representative sample of citizens in a medium-sized city in northern Italy. We found evidence that numerical, scientific, and economic literacy polarize concerns about immigration aligning them to people’s worldview orientations. Individuals with higher numerical, economic, and scientific literacy were less concerned about immigration if they held an egalitarian-communitarian worldview, while they were more concerned about immigration if they held a hierarchical-individualistic worldview. On the contrary, individuals with less numerical, economic, and scientific literacy did not show a polarized perception of immigration. Results reveal that citizens with higher knowledge and ability presented a more polarized perception of immigration. Conclusions highlight the central role of cultural worldviews over information theories in shaping concerns about immigration.

In the framework of the presented simulation, we consider a quantitative variable z (mean of 12 items) and a binary variable z2 that split out the cases in 2 worldview groups: right-oriented (when z2=1) and left-oriented (when z2=0). The variable z2 has been obtained dichotomizing the variable z based on a cut-off equal to 2.5 (the value 2.5 is assigned to the left-oriented). In the following, it is reported the contingency table of the cases. The model Consider the following modelŷ = 3.15 + 0.12x − 0.15z − 0.12xz where z is a binary variable identifying two distinct sub-populations (groups), which we call A (z = 1, i.e. right-oriented) and B (z = 0, left-oriented).
It is important to remark that these two sub-populations exist a priori. The model mirrors the regression model estimated in the paper on the data collected by the survey (for the model output, see the main text).
Therefore, two distinct regression lines exist: • the first, related to the group A (right-oriented), is:ŷ A = 3 • the second, related to the group B (left-oriented), is:ŷ B = 3.15 + 0.12x.
Hence, in the group A (right-oriented) the correlation between x and the dependent variable y is null, while in the group B (left-oriented) the correlation is greater than zero (given the sign of the regression coefficient).
This is how basically happen in the data (although dichotomizing the quantitative variable z), considering as dependent variable the numeracy: The observed values y i have, inside each group, a systematic component (ŷ i ) and a random component (e i ); the latter follows a normal distribution with mean 0 and standard deviation 0.7 (mainly the valued obtained with our data).

The reference simulation
We generate the data, mirroring the hypothesized situation. The reference simulation is then: In the operational practice, we do not know if a unit belong to the sub-population A or to the sub-population B. We know only the numerical value of the quantitative variable (that we call u), normal distributed with mean µ A in the group A and mean µ B in the group B, with same standard deviation σ. We have that µ A > µ B (high scores are obtained by right-oriented units); for instance, we can have µ A = 3 and µ B = 2, such that the central value is 2.5. To assign a unit to the group A (right-oriented) or to the group B (left-oriented) we observe if the u value is higher or lower than 2.5: if u ≤ 2.5 we assign the unit to the group B (left-oriented), if u > 2.5 we assign the unit to group A (right-oriented).
If the two groups are well separated, the situation would not be very different than that described previously. For instance, if we had σ = 0.15 the result of the previous simulation (adapted on the basis of the values of the dichotomous quantitative variable u using the threshold 2.5) would be: s <-0.7 nrep <-40*6 # multiples of 6 x <-rep(c(0:5), each=nrep/6) # the covariate x ranges from 0 and 5 set.seed(654321) As can be seen, any classification error would not exist and the regression result would be, obviously, equal to the previous one: The regression results obtained using the quantitative variable u instead of the binary one would be more difficult to interpret, especially concerning the interpretation of the interaction among two quantitative variables. In addition, the regression coefficient of the covariate x would result almost three time (even if it is not possible a direct comparison among the two coefficients).
The function gives as output a dataframe whose columns have the following meaning: • the observed values of the dependent variable (generated according to the previously defined model); • the values of the covariate x (that are substantially fixed and equal for any simulation); • the true identification of the group membership: z = 1 for right-oriented and z = 0 for left-oriented; • the value of the quantitative variable u that allow identifying the group membership to group A (right-oriented) or to group B (left-oriented); • the dichotomous value of the quantitative variable u obtained using the fixed cutoff equal to 2.5.
The function has, in addition, some internally fixed parameters, such as the values of µ A and µ B and the standard deviation of the regression model (the standard deviation of the regression model residuals).
We verify that the results are identical to the previous ones if σ = 15: df <-job(0.15, 40*6, 654321) fit <-lm(y~x*zz, data=df); summary(fit) ##  We see what happen doubling the standard deviation (σ = 0.3): df <-job(0.30, 40*6, 654321) Now no longer exists a perfect overlap and some (a few) classification errors appear: The interaction is statistically significant for both models (but the p-value for the first model is lower than that obtained for the second, i.e. most significant).
We increase again the standard deviation, reaching up to σ = 0.4: df <-job(0.40, 40*6, 654321) The classification errors increase: Comparing the parameter estimates of the models (the first with the dichotomous variable and the second with the non-dichotomous variable), we observe now that, while for the first the interaction is still significant, the second shows a non significant value for the interaction (even if quite near to the significance limit): fit.1 <-lm(y~x*zz, data=df); tmp.1 <-summary(fit.1)$coef fit.2 <-lm(y~x*u, data=df); tmp.2 <-summary(fit.2)$coef cbind ( If we increase again the standard deviation, reaching up to σ = 0.5: df <-job(0.50, 40*6, 654321) It is confirmed a statistically significant interaction for the model with the dichotomous variable (even if with a p-value lower than that observed in the previous simulation), while the model that considers the non-dichotomous variable shows, concerning the interaction estimate, a value definitely not significant: fit.1 <-lm(y~x*zz, data=df); tmp.1 <-summary(fit.1)$coef fit.2 <-lm(y~x*u, data=df); tmp.2 <-summary(fit.2)$coef cbind (